The determination of the orientation of an object's axes relative to a reference system is often of interest. Depending on the application, the orientation and reference system may be in two dimensions (2D) or in three dimensions (3D). In the case of two-dimensional systems, terms such as azimuth, heading, elevation, pitch, and inclination may be used in place of attitude.
There are many techniques in use to measure 2D and 3D attitude. Common techniques include using a magnetic compass to reference the object of interest to the local gravitational field, optical techniques to reference the object of interest to an earth-based or star-based reference frame, accelerometers to measure relative attitude or changes in attitude, and optical and mechanical gyroscopes for also measuring relative attitude. The merits of each technique are best judged according to the specific application or use. Likewise, each technique also exhibits disadvantages that may include accuracy, cost, and ease of use.
Recently, attitude determination using highly accurate space-based radio navigation systems has become possible. Such a radio navigation system is commonly referred to as a Global Navigation Satellite System (GNSS). A GNSS includes a network of satellites that broadcast radio signals, enabling a user to determine the location of a receiving antenna with a high degree of accuracy. To determine the attitude of an object, it is simply necessary to determine the position of two or more receiving antennas that have known placements relative to an object. Examples of GNSS systems include Navstar Global Positioning System (GPS), established by the United States; Globalnaya Navigatsionnay Sputnikovaya Sistema, or Global Orbiting Navigation Satellite System (GLONASS), established by the Russian Federation and similar in concept to GPS; and Galileo, also similar to GPS but created by the European Community and slated for full operational capacity in 2008.
Should it be necessary to improve the accuracy, reliability, or confidence level of an attitude or position determined through use of a GNSS, a Satellite-Based Augmentation System (SBAS) may be incorporated if one that is suitable is available. There are several public SBAS that work with GPS. These include Wide Area Augmentation System (WAAS), developed by the United States' Federal Aviation Authority, European Geostationary Navigation Overlay Service (EGNOS), developed by the European Community, as well as other public and private pay-for-service systems.
Currently the best-known of the available GNSS, GPS was developed by the United States government and has a constellation of 24 satellites in 6 orbital planes at an altitude of approximately 26,500 km. The first satellite was launched in February 1978. Initial Operational Capability (IOC) for the GPS was declared in December 1993. Each satellite continuously transmits microwave L-band radio signals in two frequency bands, L1 (1575.42 MHz) and L2 (1227.6 MHz). The L1 and L2 signals are phase shifted, or modulated, by one or more binary codes. These binary codes provide timing patterns relative to the satellite's onboard precision clock (synchronized to other satellites and to a ground reference through a ground-based control segment), in addition to a navigation message giving the precise orbital position of each satellite, clock correction information, and other system parameters.
The binary codes providing the timing information are called the C/A Code, or coarse acquisition code, and the P-code, or precise code. The C/A Code is a 1 MHz Pseudo Random Noise (PRN) code modulating the phase of the L1 signal and repeating every 1023 bits (one millisecond). The P-Code is also a PRN code, but modulates the phase of both the L1 and L2 signals and is a 10 MHz code repeating every seven days. These PRN codes are known patterns that can be compared to internal versions in the receiver. The GNSS receiver is able to compute an unambiguous range to each satellite by determining the time-shift necessary to align the internal code to the broadcast code. Since both the C/A Code and the P-Code have a relatively long “wavelength”—approximately 300 meters (or 1 microsecond) for the C/A Code and 30 meters (or 1/10 microsecond) for the P-Code, positions computed using them have a relatively coarse level of resolution.
To improve the positional accuracy provided by use of the C/A Code and the P-Code, a receiver may take advantage of the carrier component of the L1 or L2 signal. The term “carrier”, as used herein, refers to the dominant spectral component remaining in the radio signal after the spectral content resulting from the modulating PRN digital codes has been removed (e.g., from the C/A Code and the P-Code). The L1 and L2 carrier signals have wavelengths of about 19 centimeters and 24 centimeters, respectively. The GPS receiver is able to track these carrier signals and measure the carrier phase to a small fraction of a complete wavelength, permitting range measurement to an accuracy of less than a centimeter.
A technique to improve accuracy is realized by differencing GPS range measurements—known as Differential GPS (DGPS). The combination of DGPS with precise measurements of carrier phase leads to differential position accuracies of less than one centimeter root-mean-squared (i.e., centimeter-level positioning). Such accuracies are sufficient to determine the attitude of an object with 2 or more GPS GNSS antennas, typically spaced from 0.2 meters to 2 meters apart.
Accurate differential carrier phase is a primary concern for attitude determination or other precise GNSS positioning. Carrier phase data is available by tracking the carrier phase on either the L1 or L2 GPS signal. Navigation data is BPSK modulated onto both the L1 and the L2 carrier at a 50 Hz rate and, as such, the input carrier phase is subject to a 180 degree phase reversal every 20 milliseconds and the absolute phase can be inverted. The data modulation is removed from the carrier by means of a tracking loop known as a Costas loop.
A Costas loop results in a 180 degree phase ambiguity. That is, the Costas loop is just as likely to phase lock so that the binary 1's come out as binary 0's, and vice versa. The 180 degree phase ambiguity is of concern since it introduces an ambiguity of ½ of a carrier wavelength in the measured carrier phase. The wavelength of the L1 carrier is about 19 cm and the ½ cycle ambiguity is thus equivalent to 9.5 cm of measured phase.
Typically, in GPS receivers, the ½ cycle ambiguity is resolved by looking at certain data bits within the navigation message that are of a known value. If the bit is inverted over its known value, then the Costas loop is locked to the opposite phase and ½ cycle's worth of phase must be added to (or subtracted from) the measured carrier phase in order to maintain whole cycle phase alignment. It is of little consequence whether the ½ cycle is added or subtracted from the measured phase since, regardless, a whole cycle ambiguity is still present that must be removed by methods such as those described in U.S. Pat. No. 6,469,663 and/or U.S. patent application Ser. No. 11/243,112, entitled Attitude Determination Exploiting Geometry Constraints, to Whitehead et al., filed Oct. 4, 2005.
One problem that arises is that known data bits, such as those in the navigation message's preamble, arrive only so often. For example, the preamble itself is sent once every six seconds as the start of a 300 bit long sub-frame (see ICD-GPS-200). Other bits within the navigation message are known, or can be inferred from past data, but there are still many bits which are not known or which may not be predicted with 100% confidence. If the Costas loop is stressed (due to multipath fading, foliage attenuation, signal blockage, and the like) while the unknown bits are arriving, it may undergo a 180 degree phase shift that is not immediately detected. Hence, a ½ cycle error will arise in the measured phase that will persist until the next known data bit arrives. This may then reduce the accuracy in heading, pitch, or roll if the measured phase is used in an attitude determining device.
A further complication of a Costas loop is that the probability for a cycle slip is significantly higher when using a Costas loop as opposed to a conventional Phase Lock Loop (PLL). This is because the Costas loop is mathematically equivalent to a squaring loop that tracks the carrier phase at twice the carrier frequency. Phase tracking errors greater than 90 degrees may cause cycle slips in a Costas loop whereas phase errors of up to 180 degrees may be tolerated when using a PLL.
In an attitude system, such as that disclosed in Whitehead et al., the carrier phases arriving at two or more separate antennas are differenced with one another to create a differential carrier phase. The process of taking the difference cancels common mode errors such as satellite clock error and errors caused by propagation delays as the GNSS signal travels through the ionosphere and troposphere.
What is needed then is a Costas loop method that results in common ½ cycle ambiguity for carrier phases measured at both a master antenna and one or more slave antennas for a particular satellite. Being common, the ½ cycle ambiguity will cancel in the differential carrier phase.
Secondly, what is also needed is a method to make up for the loss of performance of a Costas loop over a conventional PLL. Again, since differencing is deployed, it is desirable that any cycle slips that arise on a carrier signal tracked from one antenna be present in the carrier signal tracked by a different antenna. Such cycle slips will cancel in the difference and will not affect the attitude or heading.
Thirdly, a method is needed that yields common, noise-induced effects in each individually tracked carrier phase so that the common-mode effects cancel in the differential carrier phase. A method with the aforementioned properties is applied to carrier tracking loops receiving data at two or more antennas that experience roughly similar motion or motion for which relative dynamic effects are low. The method further has the ability to track rapid clock-induced carrier phase when a common clock is employed.